Lesson 5 - Integration of Trigonometric Functions

Lesson 5 - Integration of Trigonometric Functions - dx x 2...

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ANTIDERIVATIVES (INTEGRAL)
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THE BASIC TRIGONOMETRIC INTEGRATION FORMULAS OBJECTIVES: recall and apply the different trigonometric identities in simplifying a function; and integrate trigonometric functions using their differentials as the basis for evaluation
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ASIC TRIGONOMETRIC FORMULAS From the differentials of the trigonometric functions, we derived the following integration formulas: C u tan u sec ln du u sec 5. C u csc - du u cot cscu 10. C sinu ln du u cot 4. C u sec du tanu secu 9. C cosu ln du u tan C u cot - du u csc 8. C secu ln du u tan 3. C u tan du u sec 7. C u sin du u cos . 2 C u cot u csc ln du u csc 6. C u cos du u sin . 1 2 2 + + = + = + = + = + - = + = + = + = + = + - = + - =
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TRIGONOMETRIC IDENTITIES : Reciprocal Identities : u tan 1 u cot . 6 u csc 1 u tan . 3 cu cos 1 u sec . 5 u sec 1 u cos . 2 u sin 1 u csc . 4 u csc 1 u sin . 1 = = = = = = Pythagorean Identities: u ccs 1 u cot . 3 u sec u tan 1 . 2 1 u cos u sin . 1 2 2 2 2 2 2 = + = + = +
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TRIGONOMETRIC IDENTITIES : Double Angle Identities: u tan 1 u tan 2 u 2 tan . 3 u sin 2 1 1 - u cos 2 u sin - u cos u 2 cos . 2 cosu sinu 2 u 2 sin . 1 2 2 2 2 2 - = - = = = = Half-Angle Identities: ( 29 ( 29 u 2 cos 1 2 1 u sin . 2 u 2 cos 1 2 1 u cos . 1 2 2 - = + =
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EXAMPLE - - + +
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Unformatted text preview: dx x 2 cos x 2 sin-1 9. dx 4x) sec 4x (csc 8. dx x cos x sin x cos . 4 dx 1) lnx x(csc 2-lnx csc 7. xdx 3 cos x 3 sin 5 . 3 dx x 2 cos x 2 sin 1 6. dx x 1 csc x 5 . 2 dx x 4 sin log x 4 cot 5.x dx e sin e . 1 4 4 2 2 2 2 2 x 1 cos 2 2-x 2 x 2 Evaluate the following integral. -dx 1 x 2 sin 5 . 1 2 x 2 tan + + dx x 3 cot 1 x 3 cos 2 3 . 2 2 3 -dx 2 x cot 2 x tan . 3 2 dx x 2 sin 4 . 4 x 2 sec 5 log 2 -+--dx x 2 cos 1 x 2 x cot x . 5 2 1 1 -+ dx x 2 sin 1 1 x 2 sin . 6 ( 29 --dx x / 3 csc 1 x 2 . 7 2 -+ dx 1 x 2 sin 2 x 2 cos . 8 2 2 + dx e tan 1 e csc log e . 9 x 2 x 2 x dx xe . 10 2 x sec ln XERCISES: Evaluate each of the following integral...
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Lesson 5 - Integration of Trigonometric Functions - dx x 2...

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